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Extremal and optimal properties of B-bases Collocation Matrices

Numerical Analysis 2024-12-20 v1 Numerical Analysis

Abstract

Totally positive matrices are related with the shape preserving representations of a space of functions. The normalized B-basis of the space has optimal shape preserving properties. B-splines and rational Bernstein bases are examples of normalized B-bases. Some results on the optimal conditioning and on extremal properties of the minimal eigenvalue and singular value of the collocation matrices of normalized B-bases are proved. Numerical examples confirm the theoretical results and answer related questions.

Keywords

Cite

@article{arxiv.1901.09768,
  title  = {Extremal and optimal properties of B-bases Collocation Matrices},
  author = {Jorge Delgado and J. M. Peña},
  journal= {arXiv preprint arXiv:1901.09768},
  year   = {2024}
}

Comments

11 pages

R2 v1 2026-06-23T07:24:15.251Z